# Page:CarmichealMass.djvu/13

principles for each of which there is strong experimental confirmation. This important conclusion has often been pointed out.

To the present writer, however, it seems that one point especially should be subjected to further examination. Is it in fact true that the charge of a moving electron is independent of the velocity with which it moves? Let ${\displaystyle e_{0}}$ be the charge of the electron when at rest and denote by ${\displaystyle t\left(e_{v}\right)}$ its apparent charge when in motion with velocity v, the charge being measured by means of tests in which the line of action is perpendicular to the line of motion of the charge. In the above work we have assumed, in accordance with the usual practice, that ${\displaystyle e_{0}=t\left(e_{v}\right)}$. Suppose however that the true relation were different from this, that, in fact, we have

${\displaystyle t\left(e_{v}\right)=e_{0}{\sqrt {1-\beta ^{2}}}}$

then Bucherer's experiment would lead to the conclusion that ${\displaystyle t\left(m_{v}\right)=m_{0}}$, and thus the whole theory of relativity would be overturned. Furthermore, if any relation other than ${\displaystyle e_{0}=t\left(e_{v}\right)}$ is the true one, some modification at least of the theory of relativity would have to be made or else one would have to give up postulate ${\displaystyle C_{1}}$ which asserts the law of conservation of momentum. This result brings to notice the great importance of the question of the constancy of electric charge on the electron. We shall treat this matter further in the next section.

## § 6. Another Means for the Experimental Verification of the Theory of Relativity.

Just as theorem V. was used for the theoretical basis of Bucherer's (partial) experimental demonstration of the theory of relativity so theorem VI. may be employed as the theoretical basis of a new experimental investigation which has not yet been carried out, one which bears the same essential relation as that of Bucherer to the confirmation or disproof of the entire theory of relativity. The object of this section is to indicate the nature of this experiment.

Let ${\displaystyle e_{0}}$ denote the charge of an electron when at rest with respect to a given system of reference. When it is in motion with a velocity v let ${\displaystyle t\left(e_{v}\right)}$ and ${\displaystyle l\left(e_{v}\right)}$ be the apparent charge when measured by means of tests whose lines of action are perpendicular and parallel, respectively, to the line of motion of the electron.

If we employ, postulate ${\displaystyle C_{3}}$ we conclude that ${\displaystyle e_{0}=t\left(e_{v}\right)=l\left(e_{v}\right)}$. We shall first assume the truth of one of these relations, namely, ${\displaystyle t\left(e_{v}\right)=l\left(e_{v}\right)}$, and we shall denote the common value of these two quantities by e. Now let us suppose that some means are found for measuring both the